Super Bowl Math: 2013 Edition

It’s Super Bowl time again! And since I’m a nerd, I can find a way to link math back to pretty much anything, even sports. A lot of people just watch for the commercials, but it’s more fun if you also understand what’s going on in the game. If nothing else, you can impress your friends with some truly random trivia. Obviously this isn’t a comprehensive guide to all things related to American football, but hopefully it’ll make watching the game a bit more fun.

San Francisco 49ers logoBaltimore Ravens logoThe basics: The first Super Bowl was played on January 15, 1967. This year’s contest, Super Bowl XLVII, is between the NFC champion San Francisco 49ers and the AFC champion Baltimore Ravens. Both teams are undefeated in their Super Bowl appearances. The 49ers have won all 5 of their previous Super Bowls, and are the only team to have thus far won multiple Super Bowls without losing a single one. This is only the second trip to the Super Bowl for the Ravens; they won their first game at the end of the 2000 season. The game is also noteworthy because for the first time, the head coaches are brothers (Jim Harbaugh coaches the 49ers and John Harbaugh coaches the Ravens). The game will be played in New Orleans at the Mercedes-Benz Superdome, which has been extensively repaired after being damaged by Hurricane Katrina in 2005. Unlike in most sports championships, there is no true home team in the Super Bowl; rather, the AFC team is designated the home team in even years and the NFC team is the home team in odd years. The venue is selected several years in advance of the game and no team has ever played a Super Bowl in their own stadium (though it is possible for a host team to compete in the Super Bowl, it just hasn’t happened yet). Traditionally only stadiums in warm climates or that have domes or retractable roofs have been selected to host the championship game, but this will finally change in 2014 when the new MetLife Stadium in East Rutherford, New Jersey, hosts the game. (Insert rant about how the corporate sponsors and people rich enough to afford Super Bowl tickets don’t want to have to freeze their butts off to watch the game, whereas True Fans know that the best games are played in really shitty weather.)

The audience and ads: The Super Bowl is one of the most watched programs on American television each year. At any given point in the game, there are at least 80 to 90 million people watching it in the U.S alone. The 2012 Super Bowl had the most viewers of any program ever to air on U.S. television, with an average of over 111 million viewers at any given time during the game and up to 167 million total viewers. With such a huge audience, the advertisements are famously flashy and expensive. The cost for a 30-second ad during this year’s broadcast on CBS is about $4 million, up from last year’s average price of $3.5 million. And that doesn’t include production costs! In addition, the Mercedes-Benz Superdome has seating for potentially over 79,000 fans. Tickets are still available, but they’re gonna cost you. Nosebleed seats can be bought for a mere $1,775, whereas seats on the 50-yard line run a whopping $10,884!

Gambling: As of Monday, according to Vegas Insider the average spread given by bookies in Las Vegas favors the 49ers by 3.5 points, with the over/under at 47.5. I know, what the hell does that mean? There are three basic bets you can make on the outcome of a football game (and countless much more complicated or flat-out absurd ones, but we don’t need to get into those). The easiest is just betting on who will win the game, pure and simple. Spread betting was invented to try to even out bets placed on the favorite versus the underdog, since bookies tend to lose money when everyone bets on the favorite team and it wins. The “spread” is the result of a complicated algorithm to determine how many more points the favored team will score than the underdog. If the spread is 3.5 and the favored team wins by 4 points or more, anyone who bet on them wins, whereas if they lose or win by fewer points than the spread, those who gambled on the underdogs win their bets. The over/under refers to the total number of points they think will be scored in the game, regardless of winner, and bettors wager on whether they think the total will be higher or lower. If your friends or coworkers are betting on the game, the most common form is the Box Pool. Everyone buys squares on a 10×10 grid, after which numbers from 0-9 are randomly assigned to each row and column and the two teams are assigned to either axis. At the end of each quarter, the person whose name matches the box assigned to the last digit of the current score wins a set amount. (If the final score is, say, 17-14 with the 49ers winning, the pool winner would be the box that falls at 49ers 7 Ravens 4.)

The game: So how does the game actually work? Each game is broken into four 15-minute-long quarters for a total of one hour of play. Wait, that’s all? Don’t they take much longer than that? Yes, an hour-long game takes about three hours to actually play once you add the time-outs, breaks to challenge calls, breaks for injuries on the field,  stopping the clock after some kinds of plays, and breaks between quarters. Of course there’s also halftime, which is usually 15 minutes long but expands to 30 minutes for the Super Bowl to give the stadium crew time to set up and take down fancy stages for the halftime show, which is starring Beyoncé (and possibly Destiny’s Child?) this year. If a game ends in a tie, an additional 15-minute quarter is played, with the first team to score winning the game during regular season games. During the playoffs, however, new rules took effect last year to make it more fair. Joel Thorman at sbnation.com explained, “In the new rules, the team that receives the ball first can only end the game via a touchdown (or the other team can end it via a safety). If they score a touchdown on their first possession, it’s over. But if they don’t score or only kick a field goal, the other team will get a chance to have the ball. After each team has had a possession, the game moves to sudden death.” If the score is still tied at the end of overtime during a regular season game it just ends with a tie, but in the playoffs the teams just have to keep playing extra quarters until somebody manages to score. (Thankfully, this doesn’t happen often.) Eleven men from each team are on the field during any given play. Each team gets four plays, or “downs” to try to move the ball forward ten yards from its initial starting point, called the line of scrimmage, or to score if they start within ten yards of the end zone. If the team accomplishes this, they start over with a new first down wherever the ball ended up; if not, the other team gets the ball.

Scoring: Points can be scored in several different ways. A touchdown is scored when a player either catches a pass inside or carries a ball into the opposing team’s endzone, and is worth 6 points. After a touchdown, the scoring team has the option to try to kick the ball through the goalposts for one extra point or to try for a two-point conversion, in which they essentially try to score a second touchdown from the 2-yard line. The kick is the safer and thus more common action; two-point conversions are usually only attempted late in the game in a last-ditch effort for extra points to win or tie the game and send it to overtime. Three points can be scored at any time during the game by attempting a field goal, in which the kicker tries to kick the ball through the goalposts from behind the line of scrimmage. The final way to score is called a safety, worth two points. This occurs when the team in possession of the ball ends the play behind their own goal line, and doesn’t happen very often at all.

So there you have it. There is quite a bit of math in football after all! Any questions? Leave ’em in the comments below. Otherwise, kickoff is at 6:30 p.m. ET on Sunday. See you at the party!

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[E] Hillary

Hillary is a giant nerd and former Mathlete. She once read large swaths of "Why Evolution is True" and a geology book aloud to her infant daughter, in the hopes of a) instilling a love of science in her from a very young age and b) boring her to sleep. After escaping the wilds of Waco, Texas and spending the next decade in NYC, she currently lives in upstate New York, where she misses being able to get decent pizza and Chinese takeout delivered to her house. She lost on Jeopardy.

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